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At least since pocket calculators were available there is an ongoing debate in math education of how meaningfull it is to continue to teach students how to calculations only using a paper and pencil. At the beginning the discussions were only about arithmetic operations but later (after CAS systems were available) also for example about calculating integrals. Many concluded that those skills are not needed anymore and one need to focus much more on solving complex problems, creative and critical thinking and mathematical modelling. Calculators or CAS were meant as tools to do the "routine" tasks described above.

[As a side note: At least in Germany I got the impression that this idea never really got implemented, because it didn't work to teach the average student complex, creative problem solving skills. Thus it ended up that exams consist of problems that are not more complex than in earlier times, but require less calculating skills thus being effectively easier]

Now, if you look at GPT4, it one sees that computers cannot only do "routine tasks", but also solve mathematical modelling problems or provide new mathematical proofs. See for example this research paper, where for example on page 40 a math olympiad problem was solved by GPT 4.

I know that currently GPT4 makes many errors and is not really reliable. But if the development goes on as fast as in the past years, this will not sooner or later not be a problem anymore.

So assume that GPT x or another AI can reliable solve such "creative" and "complex" math tasks (which are out of reach for the average high school students).

How to reasonable change the math curricula in this scenario? Are there any reasons to continue teaching math as we have done it in the past? If so, how to explain the students that it makes sense to learn those things when AI can do it better and much faster?

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    $\begingroup$ Does this answer your question? How to give exercises when students can use ChatGPT $\endgroup$
    – Dominique
    Mar 24 at 9:08
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    $\begingroup$ @Dominique: I don't think that this is a duplicate. The question you linked does not question the contents of the curriculum, but rather asks how to react to the fact that students could try to have their homework "solved" by a chatbot. The present questions seems rather to be about changes to the curriculum itself in respondence to the existence of such (more or less) advanced chatbots. $\endgroup$
    – Jochen Glueck
    Mar 24 at 11:43
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    $\begingroup$ While I tended to find the entire ChatGPT hype a bit enervating (in particular that some people seem to confuse "it will certainly become better" with "it will soon be able to do almost everything"), I begin to like the debate more and more: Apparently it makes people ask the really important questions - in this case, I'm under the impression that the underlying problem is in fact: What is actually the purpose of teaching students math in school? In any case, +1 for the question. $\endgroup$
    – Jochen Glueck
    Mar 24 at 11:57
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    $\begingroup$ After having read the reactions from Jochen and Julia, I've decided to retract my close vote. $\endgroup$
    – Dominique
    Mar 24 at 12:31
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    $\begingroup$ This is a silly question. In this scenario, almost all human labor is redundant, and all of society will be reorganized. It makes no sense to talk about what math education will look like if society will be completely different and math education now has to suit the needs of this completely unknown, hypothetical society. We're in a scenario where we are asking 'What is the purpose of school?' and need to answer that before asking 'What is the purpose of teaching math in school?' $\endgroup$
    – Alexander Woo
    Mar 24 at 21:23

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I think this is an important question. The issue, as I see it, is that for a long time learning mathematics has been promoted based on applications of mathematics. Obviously this approach fails to address the question that you raised, i.e., it cannot convince high-school students why they should learn tasks that AI can do better and faster. But let me ask another question: suppose one day AI can formulate and prove theorems in mathematics better and faster than humans. Are mathematicians going to abandon mathematics? It depends on why they do mathematics. Do mathematicians do mathematics to prove theorems? Some may, but many others do mathematics because they enjoy it. Consequently, it is reasonable to expect that many mathematicians will continue to do mathematics even if AI one day can formulate and prove theorems. One can ask the same question about music. If one day AI can compose music (it already can, to some extent) will humans stop composing music? Not if they enjoy doing it.

The point I am making is that whether the mathematics curricula should change or not is secondary. What should change before that is the way learning mathematics is promoted. If learning mathematics is promoted based on its enjoyability, rather than its applications, then in response to a high-school student who asks why should I learn tasks that AI can do better and faster, one can say because mathematics is enjoyable? Understandably, mathematics cannot suddenly become enjoyable by just telling people that it is enjoyable and a lot of thought and work is needed to make it enjoyable, which may include changing the curriculum.

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  • $\begingroup$ I'm hazy on the distinction being made between "prove theorems" and "do mathematics because they enjoy it". E.g., Chair of U. Chicago math department welcoming a new faculty member: "Remember: Our job is proving theorems" (per Krantz, How to Teach Mathematics 3E, Sec. 6.1). $\endgroup$
    – Daniel R. Collins
    Mar 25 at 5:11
  • $\begingroup$ "suppose one day AI can formulate and prove..." when that happens, formulating and proving theorems will not be part of the job of a mathematicians anymore. $\endgroup$
    – Michael Bächtold
    Mar 25 at 17:37
  • $\begingroup$ @DanielR.Collins A mathematical theorem is a true statement about certain mathematical objects. A proof often uses certain tools. So before one can state and prove a mathematical theorem, objects must be defined and tools must be built. When mathematicians defined manifolds, categories, schemes, topological spaces, homotopy groups, etc., they were not proving theorems. Mathematical induction, reduction mod a prime number p, infinite descent, etc., are tools that have been built to be used in proofs. Finally, some mathematicians formulate important conjectures, even though they can't prove it! $\endgroup$
    – Mahdi Majidi-Zolbanin
    Mar 25 at 17:46
  • $\begingroup$ @MichaelBächtold For comparison, AI can play chess. Did humans stop playing chess when computers learned how to play chess? Why do humans still play chess, when computers can beat most humans in chess? When we say AI can formulate and prove theorems, I don't think we mean AI is capable of proving every mathematical statement. I think at best, AI will become a tough competitor to human mathematicians. $\endgroup$
    – Mahdi Majidi-Zolbanin
    Mar 25 at 17:48
  • $\begingroup$ Perhaps the job of future mathematicians will become to prove theorems that AI cannot prove! $\endgroup$
    – Mahdi Majidi-Zolbanin
    Mar 25 at 17:55
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Tangentially related comment based on this quote:

George Carrier, who was a rare double electee to both the National Academy of Science and the National Academy of Engineering, advised his students that there were three ways to learn:

Precept 2 (Carrier’s Three Modes of Information Acquisition).

  1. Run up and down the hallway, asking, until you find a human source. [BEST]
  2. Scour the library and look it up in a book or journal.
  3. Work it out yourself. [WORST]

— J.P. Boyd, Solving Transcendental Equations

I suppose we could update these to their virtual 21st-century equivalents:

  1. Ask on StackExchange, etc.
  2. Ask ChatGPT.
  3. Work it out yourself.

Perhaps someday, 2 will overtake 1.

Boyd goes on:

Repeating previously published research yourself is the best, not worst, in terms of deeply learning a subject, but it is the worst in terms of time expenditure. Albert Migliori’s bon mot: “Six months in the lab can save you a day in the library” is equally true if “in the lab” is replaced by “deriving special methods.”

My English teacher, who had completed a Ph.D. mid-career, in high school said something similar.

Boyd presents a choice, one that relates to the question at hand: When is it worth the time to deepen your knowledge and when is it better to just get the job done? We have all made each of these choices at different times, I imagine. I imagine that given the same choices, the best choice for each person can vary.

However, I don't really see how to answer this question at this time (the curriculum question in the OP, what students should learn deeply, what tasks they should be trained to perform).

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